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JNBirDy
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Hi, this problem is from 'Electromagnetism' by Grant & Phillips and it states,
'http://i1129.photobucket.com/albums/m505/physicsbird1/126fig.png" shows a cross-section of the cylindrical high-voltage terminal of a van der Graaff generator, surrounded by an 'intershield' and a pressure vessel, both of which are also cylindrical. The gas in the pressure vessel breaks down in electric fields greater than 1.6 x 10^{7} volts/m. If the radii of the terminal, intershield and pressure vessel are 1.5 m, 2.5 m and 4 m respectively, what is the highest potential difference that can be maintained between the terminal and the pressure vessel?'
The answers given in the back of the book: '31.1 MV. When the terminal is at this voltage the intershield must be at 18.8MV to prevent breakdown.'
d∅ = -E\bulletdr
E = q/4πε₀r^{2}
1.6x10^{7} = q/4πε₀(2.5)^{2}
1.00x10^{8} = q/4πε₀ (Let q/4πε₀ = A)
A = 1.00x10^{8}
∅_{B} - ∅_{A} = -1.00x10^{8}\int^{4}_{1.5}(1/r^{2})
= -1.00x10^{8}[-1/r]^{4}_{1.5}<br /> <br /> = -1.00x10^{8} [-1/4 + 1/1.5]<br /> <br /> = -4.17x10^{7}<br /> <br /> So... can anybody tell me where I've went wrong?
Homework Statement
'http://i1129.photobucket.com/albums/m505/physicsbird1/126fig.png" shows a cross-section of the cylindrical high-voltage terminal of a van der Graaff generator, surrounded by an 'intershield' and a pressure vessel, both of which are also cylindrical. The gas in the pressure vessel breaks down in electric fields greater than 1.6 x 10^{7} volts/m. If the radii of the terminal, intershield and pressure vessel are 1.5 m, 2.5 m and 4 m respectively, what is the highest potential difference that can be maintained between the terminal and the pressure vessel?'
The answers given in the back of the book: '31.1 MV. When the terminal is at this voltage the intershield must be at 18.8MV to prevent breakdown.'
Homework Equations
d∅ = -E\bulletdr
E = q/4πε₀r^{2}
The Attempt at a Solution
1.6x10^{7} = q/4πε₀(2.5)^{2}
1.00x10^{8} = q/4πε₀ (Let q/4πε₀ = A)
A = 1.00x10^{8}
∅_{B} - ∅_{A} = -1.00x10^{8}\int^{4}_{1.5}(1/r^{2})
= -1.00x10^{8}[-1/r]^{4}_{1.5}<br /> <br /> = -1.00x10^{8} [-1/4 + 1/1.5]<br /> <br /> = -4.17x10^{7}<br /> <br /> So... can anybody tell me where I've went wrong?
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